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This is just an update on my last post about maths prep for OU’s MST124 module.  Altogether I’ve given it about two and a half weeks of study and revision, and I feel completely confident with my level of maths going into MST124.

I think my breakthrough occurred when I decided that I probably should stop trying complex equations in my head or doodling on my screen with the mouse.  It was when I pulled out a pad of paper and a pen that it all slotted into place, and it turned out my brain hadn’t completely liquefied in the several decades since I’d left school; It was just super lazy.  Not a shocking realisation, then.

So I’m nearly back up to the level I was when I dropped out of high school, with exponential and logarithm manipulation added to my tool belt.  (Learning logarithms was way cool, but the Khan Academy model wasn’t set out in the most logical order.  It took going back to the beginning after I’d gotten halfway through and learned bits and pieces from other sites.)

I went back onto the OU’s Maths Choices MST124 diagnostic Are You Ready quiz last night, and this time ran away with full marks in less than 15 minutes.  A dramatic increase on the 40-something minutes it took last year for 70- or 80-something percent.  Still, that’s simply being able to crunch the numbers.  If they were to throw words like “justify” or “explain” I’d be reduced to the sludge in the bottom of my vegetable “crisper” in no time.  So I still have plenty to do this summer in terms of getting proofs down and maybe skipping a bit ahead so I’m not taken off guard.

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When deciding between the MU123 and MST124 maths modules for my degree, I put a fair amount of weight on the diagnostic “Are you ready?” quiz for MST124.  It said my results were good, there were a few areas I should brush up on, but overall I should be just fine on it.

I won’t start the module until 7 October, so I’ll have to wait until then before I throw their pants doused with lighter fluid onto a telephone wire and chanting, “Burn, liar!  Burn!”

I just don’t know how prepared I really am.  See, the OU have opened up a “revise and refresh” website for MST124.  It’s amazing that they even do that.  It has diagnostic quizzes with typical questions one might encounter on various MU123 blocks.  Depending on how well you do on that, they have some cheat sheets for reminding you how to solve certain problems.  (It keeps referring me to read blocks from MU123 … Uh … probably not worth it to buy the books on eBay.)

When I do those, I perform a bit better than I did on the MST124 AYR quiz.  I note my weak areas, I study the sheets, and I do better.  But it kept feeling like it was only checking a very, very narrow section of maths at that level.

So I went to my original plan for MST124 preparation: Khan Academy!  (I can’t say enough good things about this site.  My older son enjoys it about as much as he enjoys Roblox.)  I’ve been working over there for about a week, now, shoring up as many weak spots as I can find, but that list keeps getting longer, and longer, and longer.  The site can hone in on your weaknesses the way painkiller commercials claim their product can.  And the areas of study can be very, very specific.  Like … “Sinusoidal models word problems“.  I have to decipher it before I can decide whether or not I know it and/or need it.  (I apparently do know it.  But good luck ever getting me to recognise it.)

They’re not that difficult to study, it’s just that there’s SO MANY OF THEM!  I’ve “mastered” something like 650 identified skills, and have more than 500 to go.  Granted, that’s for all the maths they can currently teach and evaluate on Khan Academy.  I won’t need anywhere near all of them by the time I start MST124.  But the skills can sometimes take an entire night.  I’ve got a hundred and thirtysomeodd days until the module starts, and a lot of those are on holiday.  In a lot of ways, the pre-study preparation feels harder than TU100 was.

Unlike TU100, though, I’m learning tons, not just practising.  And the practise is definitely necessary to get me into fighting shape again for the module.  And more practise.  And some more.  And it’s also fun.  But that part isn’t different from TU100.  I’ve really enjoyed my journey so far.

I won’t know until after I’m in the middle of it which was better for preparation: The OU MST124 preparation site, designed specifically for it, or Khan Academy, which is pretty much drinking from the fire hose.  Or Niagara Falls.  We’ll see how it goes.

One final bit for today: Results for TU100 will be in on 19 July.  My tutor will give us a cheeky heads-up if we passed or not before that, but nothing more.

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After five days of websites, phone calls, and emails, I’m finally enrolled on my next modules for Q62.  I’m finishing out Stage 1 with TM129 (Technologies in practice) and MST124 (Essential mathematics 1).  Enrolment for October 2017 opened on the 9th, and it finally got completely sorted this morning.  The website wouldn’t let me register on the first day, because it thought I was trying to take the modules in America from a UK address.  I don’t even know what that means, but I had to call the next day to sort it out.  Once they corrected that issue, they said I hadn’t sent in proof of residence in the UK.  Finding it pointless to argue what had or hadn’t been done, versus what had or hadn’t been lost by their IT systems, I sent in more proof.  The next hurtle was that they registered me on the phone for the modules, but didn’t tie those modules to my degree, so they wouldn’t count toward it.  (In the long run, this isn’t an issue, but it would have required more fuss next year, since my Stage 1 wouldn’t be cleared, even though I’d taken all the required modules.)  Student Finance England should start taking applications for part-time studies in the 2017/2018 academic year in around mid-May, but putting my SFE CR number in now switched me from just reserving the spot in the module until 20 April to being fully registered in it.

As with TU100, I will be on one of TM129’s final presentations.  The module’s final run is October 2018, but I think it has a February 2018 run before that.  It covers three main areas: Networking, Linux, and Robotics.  I’m glad that the degree is rounding out the ICT experience of its programme with these areas.  I’m extremely familiar with the first two, and a very poor hobbyist in the third.  My six year old son helped me build little toy robots last year, and this year he’s been working with a brilliant snap-together circuitry kit his auntie in America got him for Christmas.  Even though the practical portions of the robotics section is entirely virtual, I’m certain he’ll enjoy sharing those parts together.  It also comes with a copy of Isaac Asimov’s I, Robot, which was one of my favourite books in seventh grade.

MST124, I’m not ashamed to say, is a bit outside my abilities.  I will not be receiving a distinction on this module.  As only a bare pass is required and the specific outcome does not impact my degree classification in the slightest, I’m using this to full advantage and studying something I know I’ll only do about average on.  The trade-off is that I should learn and grow the most with this module.

I’ve finally found the block descriptions for MU123 and MST124, so here’s what you learn:

MU123

  • Basic maths review
  • Vocabulary and notation
  • Types of numbers
  • Statistical summaries (types of averages, significant figures, etc.)
  • Algebra
  • Graphs
  • Inequalities
  • Geometry
  • Advanced algebra
  • Quadratics
  • Statistical pictures
  • Trigonometry
  • Exponentials
  • “Maths everywhere” (which I’m guessing is making it practical, which means story problems)

MST124

  • Algebra review
  • Graphs and equations review
  • Functions
  • Trigonometry review
  • Coordinate geometry and vectors
  • Differentiation
  • Differentiation methods and integration
  • Integration methods
  • Matrices
  • Sequences and series
  • Taylor polynomials
  • Complex numbers

Now, why the OU can’t just put this list side-by-side someplace and let people choose is beyond me.  Looking at this, I can see that I had cleared MU123 by the ninth grade, including the level of trigonometry taught there.  I’m about halfway up the MST124 list, having done some differential calculus, but in dire need of a refresher.  I would be bored to tears on MU123.  So even though I’m quite certain I’ll get toward the lower end of between 40% and 84% on my end-of-module exam, MST124’s my route.  (I’ve heard the exam is multiple choice, though, so anything’s possible.)

It also has a revise & review site that opens up next week for early registrants to prepare them in case we’ve forgotten as much maths as we’ve learned.

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Edit 14/03/2017: I’ve added the block contents of the two modules in another post, so you can finally compare which concepts you do or don’t have.

The question of which maths module to take is one that comes up a fair bit for students of the Open University, especially in STEM degrees.  It comes up so often, in fact, that the OU has a site devoted to the question.  For most people, this will mean choosing between MU123 (Discovering Mathematics) and the more difficult MST124 (Essential Mathematics I).

For some degrees, such as Maths, Physics, or Engineering degrees, the question is merely one of where you should start, as you’ll likely need to take and pass MST124 anyway at some point along your path. But for other degrees, you’re simply required to take a maths class, and which of the two you choose is completely up to you, with no effect on your degree or its classification.

As they’re Stage 1 modules, your pass level won’t affect classification. However, MU123 has a basic pass/fail structure, while MST124 allows the awarding of a distinction. I wouldn’t think this at all important, but someone pointed out that if they apply for a job while still on the degree course, it might be nice to say they passed all Stage 1 modules with a distinction.

I’ve mentioned earlier that I’m A) an immigrant, and B) a drop-out, so that makes deciding which maths to go into more difficult.  I was in advanced maths when I dropped out of high school early.  This would have meant I finished with the same amount of maths as non-advanced maths, but still beyond the compulsory amount required for all students. But I also skipped a year of maths before that, and had to self-teach some. So I’m left trying to match that up with “GCSE Maths” and “A-Level Maths” without anybody realising that the curriculum changes from time to time.  It would be so much easier if they simply said which mathematical concepts you needed to be familiar and comfortable with.

When I took the practice quizzes at the above mentioned site, I breezed through the MU123 quiz. When I took the MST124 quiz, I did alright through the first half of the questions, but it was taking me forever to remember formulas and rules I haven’t used in twenty years.  And the questions just felt tedious.  And I figured I just didn’t need that in my life.  So I didn’t even complete it.

Since it doesn’t make a difference to my degree, and it will be easier for me to get through and not burn me out, I was all set to simply take MU123 next year and never look back.  Working in the industry for as long as I have, I’m fairly certain it won’t ever come up in my job.

That was, however, before I encountered the Hitbox.

On a great series of MOOCs that I’m doing, I’m currently coding some graphics programmes. In all of the practice programmes we’re assigned so far, it asks us to only concern ourselves with the center point of the image, and pretend that if the image wanders halfway off the side of the screen, that’s still within the boundary of the screen.

I wanted to do it a little more advanced.  For instance, if the image is approaching the edge of a screen at a right angle, it can get as close as 1/2 the image size distance between the center-point and the screen boundary.  Easy enough to code that

But what if it’s approaching the boundary at an angle?  Now the corner of my image is further in the X or Y coordinate than half the image height or width.  How do I figure that out?

Well, it’s simple trigonometry.  As I mentioned the other week, I was self-taught in trig until last month, so I got a close look at a practical issue to see how well I understood it.  Here’s how I sketched out my problem:

hitbox-problem

 

It’s clear to see that the closest I can get to the top edge on the Y axis is going to be the distance between the center of my image and the corner of the image (also calculated using simple trigonometry) multiplied by the cosine of the indicated angle.  Cosine(y) = Adjacent Y/Hypotenuse Y, so Hypotenuse Y * Cosine(y) = Adjacent Y.  Similarly, I need that same hypotenuse (all corners will be the same distance away from the center in a square or rectangular image) multiplied by Cosine(x) to determine how close I can get along the X axis.

So that’s all pretty basic-level maths.  But it’s a very basic hitbox, too.  What if I don’t want to pretend my images are rectangles?  What if I’m having a scalene triangle interact with an irregular pentagon?  (Adding a third dimension isn’t really all that different, you just have to increase the number of checks that are made and the calculations that represent edges.)

It’s still not that difficult to calculate hitboxes, as it becomes a series of intercepting slopes being greater than or less than line segment points.  But the hitbox is just one tiny thing to calculate. And already my shortcomings in maths could have hampered a solution if I hadn’t prepared myself.

So I think I’m now edging toward MST124. To be clear, I don’t plan to go into programming, and though I’d love a proper Computer Science degree, this is as close as the Open University gets.  But I would like to have as many bases covered as possible, and not regret that I should have had more maths under my belt when I come across something I hadn’t considered in the future.  Besides, I did go back and finish the MST124 Are You Ready quiz, and it agrees that it’s a decent fit.